Multi-digit multiplication

Multi-digit multiplication: More than just the traditional algorithm

Multi-digit multiplication isn't the focus of this course, but doing multi-digit multiplication provides practice for students in their multiplication combinations (even though it is much more complex than just knowing the multiplication facts). Some advice about teaching multi-digit multiplication is included here, as a next step beyond learning the fact families.

You can use this handout to assess students' understanding of multi-digit multiplication: Handout 7: Multi-digit multiplication practice problems. Or use this teacher background paper to analyze students' difficulties with multi-digit multiplication: Analyzing computation difficulties

There are several key concepts that students need to master, in order to be fluent with multi-digit multiplication and multi-digit division. They are explained in detail in this background paper: Multiplication and division learning progression.

In short, to get to the point of being able to fluently multiply any two whole numbers, students should

1. Know that the concept of multiplication is repeated adding or skip counting – finding the total number of objects in a set of equal size groups (N.ME.02.04 and N.MR.02.13)
2. Be able to represent situations involving groups of equal size with objects, words and symbols. (N.MR.02.16)
3. Know multiplication combinations fluently (which may mean some flexible use of derived strategies).
4. Know how to multiply by 10 and 100. (N.FL.03.13)
5. Use number sense to estimate the result of multiplying.
6. Use arrays and area models to represent multiplication (N.MR.02.14) and to simplify calculations.
7. Understand how the distributive property works and use it to simplify calculations. (N.ME.04.09 Multiply two-digit numbers by 2, 3, 4, and 5, using the distributive property…) For example: 46 x 5 = (40 x 5) + (6 x 5) = 200 + 30.
8. Use alternative algorithms like the partial product method (based on the distributive property) and the lattice method.
9. Identify typical errors that occur when using the standard algorithm. (N.FL.05.04) For example, see if you can figure out this:

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Multi-digit multiplication learning progression